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|Title||Topological Properties For Digital Spaces|
|Title in Arabic||الخصائص التوبولوجية للفراغات الرقمية|
In this thesis, we study the digital spaces Zd, d ∈ N, and their topological properties.We show that there are only one topology on Z, two topologies on Z2, and five topologies on Z3 whose (topological) connected sets are graphicly connected. We prove that these topologies are a generalized locally finite T0-Alexandroff spaces. Up to this fact, some of the basic concepts and results that are involved in ,  and  are studied on these topologies. We describe the orders induced on these topologies and the relations between them. To take advantage of our results we applied them in the digital label images. Some of the important results are finding Marcus -Wyse function and 2,3-AlexandroffHopf functions. We prove that the Alexandroff-Hopf topology on Z2 (resp. on Z3) is the product topology of two ( resp. three) Khalimsky topologies on Z (resp. on Z3). We define the ith-summation topology S2 (resp. S3) and find the relationship between it and the digital topologies on Z2 (resp. on Z3). We prove that the αs-space is the dual to the β-space.
|Publisher||الجامعة الإسلامية - غزة|
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